Question:
Let \( A = \{1, 3, 7, 9, 11\} \) and \( B = \{2, 4, 5, 7, 8, 10, 12\} \). Then the total number of one-one maps \( f: A \to B \), such that \( f(1) + f(3) = 14 \), is:
Let \( A = \{1, 3, 7, 9, 11\} \) and \( B = \{2, 4, 5, 7, 8, 10, 12\} \). Then the total number of one-one maps \( f: A \to B \), such that \( f(1) + f(3) = 14 \), is:
Updated On: Jan 8, 2025
- 180
- 120
- 480
- 240
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The Correct Option is D
Solution and Explanation
Given sets:
\[ A = \{1, 3, 7, 9, 11\} \quad \text{and} \quad B = \{2, 4, 5, 7, 8, 10, 12\} \]
\[ A = \{1, 3, 7, 9, 11\} \]
\[ B = \{2, 4, 5, 7, 8, 10, 12\} \]
\[ f(1) + f(3) = 14 \]
(i) \( 2 + 12 \)
(ii) \( 4 + 10 \)
\[ 2 \times (2 \times 5 \times 4 \times 3) = 240 \]
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